#42
Top 50 Mistake
Giving probability greater than 1
"The Impossible Probability"
The Mistake in Action
A bag contains 3 red and 5 blue balls. Find P(red).
Student writes: "P(red) = 3/5 = 1.6"
Why It Happens
Students sometimes divide the wrong way around, or confuse probability with odds. They might divide favourable by unfavourable instead of favourable by total.
The Fix
Probability is always between 0 and 1 (inclusive).
Check your answer: If you get something greater than 1 or negative, something is wrong!
Correct: $P(\text{red}) = \frac{3}{3+5} = \frac{3}{8}$
The denominator is always the TOTAL number of outcomes, not the other outcomes.
Spot the Mistake
Can you identify where this student went wrong?
Red balls = 3, Blue balls = 5
P(red) = 3/5
= 0.6
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: